Hi Jessica,
How exciting that your trip is so close - I am very jealous!
The absolutely quickest way to get from your Resort hotel to
Mickey's Backyard BBQ which is located at the Campsites at Disney's Fort Wilderness Resort would be to drive or take a taxi directly there which would take approximately 15 minutes.
If you plan on using Disney's complimentary transportation service, I would suggest that you take a bus from your Resort hotel to the Magic Kingdom theme park and then from there, take a boat over to Disney's Fort Wilderness Resort & Campground. The bus and boat journey will each take approximately 15 minutes plus you will need to allow for up to an additional 20 minutes for time which may be spent waiting for the next bus and boat to arrive.
Another thing to remember is that Guests are requested to arrive at least 30 minutes prior to show time and if you need to pick up your tickets at the show box office, you best plan on arriving 40 minutes prior to show time.
Taking all of this into consideration and to ensure that you get to Mickey's Backyard BBQ in plenty of time, I would recommend that you plan to be at the bus stop at your Resort hotel 2 hours prior to the time of your reservation.
Wishing you a magical trip filled with memories which will last a lifetime!